Novel modified distribution functions of fiber length in fiber reinforced thermoplastics

Abstract Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λα and λβ) can be considered as the linear growth function of ln. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT.